ANOTHER LOOK AT THE FAST ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM (FISTA)

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This paper provides a new way of developing the fast iterative shrinkage/thresholding algorithm (FISTA) [A. Beck and M. Teboulle, SIAM T. Imaging Sci., 2 (2009), pp. 183-202] that is widely used for minimizing composite convex functions with a nonsmooth term such as the l(1) regularizer. In particular, this paper shows that FISTA corresponds to an optimized approach to accelerating the proximal gradient method with respect to a worst-case bound of the cost function. This paper then proposes a new algorithm that is derived by instead optimizing the step coefficients of the proximal gradient method with respect to a worst-case bound of the composite gradient mapping. The proof is based on the worst-case analysis called the performance estimation problem in [Y. Drori and M. Teboulle, Math. Program., 145 (2014), pp. 451-482].
Publisher
SIAM PUBLICATIONS
Issue Date
2018
Language
English
Article Type
Article
Keywords

LINEAR INVERSE PROBLEMS; WORST-CASE PERFORMANCE; 1ST-ORDER METHODS; CONVEX-OPTIMIZATION; THRESHOLDING ALGORITHM; GRADIENT-METHOD; MINIMIZATION; CONVERGENCE

Citation

SIAM JOURNAL ON OPTIMIZATION, v.28, no.1, pp.223 - 250

ISSN
1052-6234
DOI
10.1137/16M108940X
URI
http://hdl.handle.net/10203/245442
Appears in Collection
MA-Journal Papers(저널논문)
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